Transverse vibrations of an axially accelerating viscoelastic string with geometric nonlinearity

Journal of Engineering Mathematics

Volumn 48, Issue 2, 2004, Pages 171-182

  Chen, Li Qun ^a   Zu, Jean W ^b   Wu, Jun ^a   Yang, Xiao Dong ^a  

^a SHANGHAI UNIVERSITY   (China)

^b UNIVERSITY OF TORONTO   (Canada)

Author keywords

Axially accelerating string; Geometric nonlinearity; Method of multiple scales; Stability; Viscoelasticity

Indexed keywords

HARMONIC ANALYSIS; LYAPUNOV METHODS; NONLINEAR SYSTEMS; PARTIAL DIFFERENTIAL EQUATIONS; RESONANCE;

HARMONIC VARIATION; PARAMETRIC RESONANCE;

VISCOELASTICITY;

MATHEMATICAL METHOD;

EID: 1342332025     PISSN: 00220833     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:ENGI.0000011929.17902.87     Document Type: Article

References (20)

1. C.D. Jr. Mote. Dynamic stability of axially moving materials. Shock Vibr. Digest 4 (1972) 2-11.
2. J.A. Wickert and C.D. Jr. Mote. Current research on the vibration and stability of axially-moving materials. Shock Vibr. Digest 20 (1988) 3-13.
3. A.S. Abrate, Vibration of belts and belt drives. Mechanism & Machine Theory 27 (1992) 645-659.
4. L.Q. Chen and J.W. Zu, Transverse vibration of axially moving strings and its control. Adv. Mech. 31 (2001) 535-546.
5. R.F. Fung, J.S. Huang and Y.C. Chen. The transient amplitude of the viscoelastic travelling string: an integral constitutive law. J. Sound Vibr. 201 (1997) 153-167.
6. L. Zhang and J.W. Zu, Non-linear vibrations of viscoelastic moving belts, part 1; free vibration analysis. J. Sound Vibr. 216 (1998) 75-91.
7. L. Zhang, J.W. Zu, Non-linear vibrations of viscoelastic moving belts, part 2; forced vibration analysis. J. Sound Vibr. 216 (1998) 93-105.
8. L. Zhang and J.W. Zu, Nonlinear vibration of parametrically excited moving belts, part 1: dynamic response. ASME J. Appl. Mech. 66 (1999) 396-402.
9. L. Zhang and J.W. Zu, Nonlinear vibration of parametrically excited moving belts, part 2: stability analysis. ASME J. Appl. Mech. 66 (1999) 403-409.
10. L.Q. Chen, J.W. Zu and J. Wu, Dynamic response of the parametrically excited axially moving string constituted by the Boltzmann superposition principle. Acta Mech. 162 (2003) 143-155.
11. W.J. Zhao and L.Q. Chen, A numerical algorithm for non-linear parametric vibration analysis of a viscoelastic moving belt. Int. J. Nonlin. Sci. Num. Simulations 3 (2002) 129-134.
12. J.S. Huang, R.F. Fung and C.H. Lin, Dynamic stability of a moving string undergoing three-dimensional vibration. Int. J. Mech. Sci. 37 (1995) 145-160.
13. E.M. Mochensturm, N.C. Perkins and A.G. Ulsoy. Stability and limit cycles of parametrically excited, axially moving strings. ASME J. Vibr. Acoust. 116 (1996) 346-351.
14. W.L. Miranker. The wave equation in a medium of motion. IBM J. Res. Developm. 4 (1960) 36-42.
15. M. Pakdemirli and H. Batan, Dynamic stability of a constantly accelerating string. J. Sound Vibr. 168 (1993) 371-378.
16. M. Pakdemirli, A.G. Ulsoy and A. Ceranoglu, Transverse vibration of an axially accelerating string. J. Sound Vibr. 169 (1994) 179-196.
17. M. Pakdemirli and A.G. Ulsoy, Stability analysis of an axially accelerating string. J Sound Vibr. 203 (1997) 815-832.
18. E. Ozkaya and M. Pakdemirli, Lie group theory and analytical solutions for the axially accelerating string problem. J. Sound Vibr. 230 (2000) 729-742.
19. J. Wu and L.Q. Chen. Steady-state responses and their stability of nonlinear vibration of an axially accelerating string. Appl. Math. Mech. (to be published).
20. J.A. Wickert and C.D. Jr. Mote, Classical vibration analysis of axially moving continua. ASME J. Appl. Mech. 57 (1990) 738-744.